International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 4, Pages 251-262

On Krull's intersection theorem of fuzzy ideals

V. Murali1 and B. B. Makamba2

1Department of Mathematics (Pure & Applied), Rhodes University, Grahamstown 6140, South Africa
2Department of Mathematics, University of Fort Hare, Alice 5700, South Africa

Received 11 May 2001

Copyright © 2003 V. Murali and B. B. Makamba. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We deal with Krull's intersection theorem on the ideals of a commutative Noetherian ring in the fuzzy setting. We first characterise products of finitely generated fuzzy ideals in terms of fuzzy points. Then, we study the question of uniqueness and existence of primary decompositions of fuzzy ideals. Finally, we use such decompositions and a form of Nakayama's lemma to prove the Krull intersection theorem. Fuzzy-points method on finitely generated fuzzy ideals plays a central role in the proofs.